CN110658549A - Background medium and weak signal-to-noise ratio improving method and application - Google Patents
Background medium and weak signal-to-noise ratio improving method and application Download PDFInfo
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Abstract
The invention discloses a method for improving signal-to-noise ratio of a background medium-weak signal and application, belongs to the field of weak signal identification, and aims to solve the problems that when a source signal is lower than a natural background signal, the identification of the source signal is influenced by the statistical fluctuation of the background signal, especially when the source signal is far smaller than the background signal, the influence of the background fluctuation on the signal identification is larger, and when the fluctuation amplitude of the statistical fluctuation of the background signal is equal to or larger than the quantity of the source signal, the influence of the statistical fluctuation of the source signal is added, and whether the source signal exists in measurement data or not is difficult to judge by a total counting method. Experimental results show that the zeta value method has remarkable effects on improving the signal-to-noise ratio, reducing the statistical fluctuation of signals and improving the recognition capability of weak signals in the background. At the same time, the zeta-value method of the present application depends on the energy resolution of the detector, so that it is only necessary to determine its optimum for different detectorsxValue that the best weak signal identification can be achievedOther capabilities.
Description
Technical Field
The invention relates to the field of radiation measurement, in particular to the field of weak signal identification, and specifically relates to a background medium and weak signal-to-noise ratio improving method.
Background
The natural radiation background level varies for a number of reasons (e.g., altitude, shielding, self-shielding, building structure, building material, soil type, time, season, solar activity, etc.), and can vary widely. When the source signal is lower than the natural background signal, the statistical fluctuations of the background signal will affect the identification of the source signal. Especially when the source signal is much smaller than the background signal, the fluctuation of the background has a larger influence on the signal identification. When the fluctuation amplitude of the statistical fluctuation of the background signal is equal to or larger than the amount of the source signal, and the influence of the statistical fluctuation of the source signal, whether the source signal exists in the measured data is difficult to judge by using a total counting method.
Therefore, a new method is urgently needed to solve the above problems.
Disclosure of Invention
The invention aims to: the method for improving the signal-to-noise ratio of the medium-low background signal aims at solving the problems that when the source signal is lower than the natural background signal, the statistical fluctuation of the background signal can influence the identification of the source signal, especially when the source signal is far smaller than the background signal, the influence of the background fluctuation on the signal identification is larger, and when the fluctuation amplitude of the statistical fluctuation of the background signal is equal to or larger than the amount of the source signal, the influence of the statistical fluctuation of the source signal is added, and whether the source signal exists in the measured data or not is difficult to judge by using a total counting method. Experimental results show that the zeta value method has remarkable effects on improving the signal-to-noise ratio, reducing the statistical fluctuation of signals and improving the recognition capability of weak signals in the background.
In order to achieve the purpose, the invention adopts the following technical scheme:
a background medium and weak signal to noise ratio improving method comprises the following steps:
(1) the source signal identification capability ζ of the detector is defined, as shown in the following equation (5),
in the formula, NnAs a count of background, NsCounting the source signals;
the maximum value of ζ can be found from the derivative of equation (5) being zero, i.e., d ζ is 0,
(2) x tracks are symmetrically selected around the central track address mu, and the upper domain and the lower domain are [ mu-x, mu + x]Then the source signal NsThe counts in the count interval are represented as an integral function of the track address t,
in the formula (7), NsμThe number of the channel address and the signal center is set as a constant A; the differential dN of the source signal with xsIn order to realize the purpose,
(3) let the density function of background count with track address be f (Ch), and under the condition of no other peak interference, regard the density function f (Ch) as linear variation with track address, let the background count NnHas a function of Nn＝2NnμX, then NnThe differential of (a), i.e., the density function f (ch), is shown in the following formula (9):
dNn＝2Nnμ·dx＝ f(Ch) (9)；
in the formula (9), NnμThe count of the background center track address is approximately constant and is set as C, and the following are:
dNn＝2Cdx (10)；
mixing dNsAnd dNnWhen the formula (6) is substituted, then
(4) When a proper x value is selected to satisfy the formula (10), the signal-to-noise ratio and the relative fluctuation of the counting interval can be well balanced.
In the step 1, the signal-to-noise ratio and the weight of the relative random fluctuation to the source signal identification capability are assumed to be the same.
In step 1, a source signal identification capability ζ of the detector is defined, as shown in the following formula (1),
in the formula (1), Rs/n-the signal-to-noise ratio;
κs-relative random fluctuations of the signal;
κn-relative random fluctuations in background;
setting the total count of source signal and background to NgBackground count is NnThen the source signal counts NsIn order to realize the purpose,
Ns＝Ng-Nn (2)；
thus, the source signal relative fluctuation кsAnd relative fluctuation к of backgroundnRespectively, are as follows,
in formula (3), σsNet counts fluctuations for the source signal;
in the formula (4), σnThe background fluctuation;
then, ζ can be expressed as,
the maximum value of ζ can be found from the derivative of equation (5) being zero, i.e., d ζ is 0,
in the step 4, the formula (11) is an transcendental equation, and the value x is obtained by drawing and solving curves on two sides, so that the signal-to-noise ratio and the relative fluctuation of the counting interval can be well balanced.
The method for improving the signal-to-noise ratio of the weak signal in the background is applied.
The method is used for the determination of the radiation signal.
To verify the feasibility of the present application, the inventors performed corresponding tests. After comparing a tail signal deduction method (a zeta value method, namely the background medium and weak signal to noise ratio promotion method) with a traditional full-energy peak signal method (3 sigma), the zeta value method can not only improve the signal to noise ratio, but also reduce the statistical fluctuation of signals, increase the difference between the signals and the background after the signals are superposed and the background without the signals, and greatly enhance the identification capability of the background medium and weak signals. In the experiment, x when zeta is the maximum value is found to keep better stability.
For the detector used in the embodiment of the application, x fluctuates slightly in the range of [8,10], and is hardly influenced by the source signal intensity, which shows that the zeta value method has better universality for a specific detector. Meanwhile, the zeta value method of the application depends on the energy resolution of the detector, so that the optimal weak signal identification capability can be realized only by measuring the optimal x value of different detectors.
Drawings
The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a signal versus background profile.
FIG. 2 is weak137Energy spectrum of Cs source at NaI detector.
Fig. 3 is a graph showing the change in zeta value with the counting interval x.
FIG. 4 is a graph showing the distribution of x when ζ is maximized.
FIG. 5 is a graph of zeta value as a function of x for different signal strengths.
FIG. 6 is a graph showing the relative fluctuation of signals at different source intensities for the two methods in example 1.
Fig. 7 is a graph of the signal-to-noise ratio for the two methods at different source strengths.
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
Example 1
1. The working principle of the present application is explained as follows.
When the source signal is lower than the natural background signal, the statistical fluctuations of the background signal will affect the identification of the source signal. Especially when the source signal is much smaller than the background signal, the fluctuation of the background has a larger influence on the signal identification. When the fluctuation amplitude of the statistical fluctuation of the background signal is equal to or larger than the amount of the source signal, and the influence of the statistical fluctuation of the source signal, whether the source signal exists in the measured data is difficult to judge by adopting a total counting method.
As shown in fig. 1, the signal is generally gaussian and the background is generally linear (without other peak interference). When the traditional method judges whether a signal exists in the background, the traditional method judges by analyzing the difference between the total signal (A + B + C + D + E + F) and the background (A + B + C). The signals E and F contribute less to the signal, but the background a and C contribute relatively more to the background. This results in a greater increase in statistical fluctuations after the background contains a and C, reducing the signal-to-noise ratio and the difference between the total signal and the background. As can be seen from FIG. 1, the analysis intervals are different, and the signal-to-noise ratio is different from the statistics. At full signal coverage, the signal-to-noise ratio is (D + E + F)/(a + B + C). The tail deduction method removes a small part of Gaussian tail signals, and the signal-to-noise ratio is D/B. Since E/A and F/C are smaller than D/B, it can be demonstrated that the smaller the selected interval (the smaller x), the larger the signal-to-noise ratio D/B.
The identification of the source signal is primarily related to two factors: signal to noise ratio, total count. In terms of signal-to-noise ratio, the larger the signal-to-noise ratio is, the more the source signal can be distinguished from the background signal; in terms of total counts, the total counts determine the level of random fluctuations in background and signal. The relative fluctuation of the random statistics is 1/(N ^ (1/2)) × 100%, and the total count N is determined by the measurement time. The longer the measurement time is, the lower the relative fluctuation is, which is beneficial to improving the confidence coefficient of the source signal identification rate under the condition of a certain signal-to-noise ratio. The time cannot be extended indefinitely, and the time cost and recognition rate must be balanced.
Assuming that the signal-to-noise ratio and the weight of the relative random fluctuation to the source signal identification capability are the same, the source signal identification capability ζ of the detector is defined,
in the formula (1), Rs/n-the signal-to-noise ratio;
κs-relative random fluctuations of the signal;
κn-relative random fluctuations in background.
Setting the total count of source signal and background to NgBackground count is NnThen the source signal counts NsIn order to realize the purpose,
Ns＝Ng-Nn (2)；
thus, the source signal relative fluctuation кsAnd relative fluctuation к of backgroundnRespectively, are as follows,
in formula (3), σsNet counts fluctuations for the source signal;
in the formula (4), σnBackground fluctuation.
Thus, ζ can be expressed as,
the maximum value of ζ can be found from the derivative of equation (5) being zero, i.e., d ζ is 0,
due to random fluctuation, the total energy peak is widened to a Gaussian peak by taking the characteristic energy mu as the center, x tracks are symmetrically selected around the central track address mu, and the upper domain and the lower domain are [ mu-x, mu + x [ ]]Thus, the source signal NsThe count in the count interval can be expressed as an integral function of the track address t,
in the formula (7), NsμThe count of the channel address in the signal is set to a constant A. The differential dN of the source signal with xsIn order to realize the purpose,
the background count is f (Ch) as a function of the density of the addresses. The density function f (ch) can be generally seen as a linear variation with track address without other peak interference.
The background count is f (Ch) as a function of the density of the addresses. The density function f (ch) can be generally seen as a linear variation with track address without other peak interference. In this case, the background count NnHas a function of Nn＝2Nnμ·x，NnThe differential, i.e. the density function f (ch),
dNn＝2Nnμ·dx＝ f(Ch) (9)；
in the above formula, NnμIs the count of the background center track address, is approximately constant, is set as C, then
dNn＝2Cdx (10)；
Mixing dNsAnd dNnSubstituting into the formula (6),
in the formula (11), N0Is the background of the central track address. When a proper x value is selected to satisfy the formula (11), the signal-to-noise ratio and the relative fluctuation in the counting interval can be well balanced. Equation (11) is a transcendental equation and can be solved by plotting curves on both sides.
2. Results and analysis
2.1 Zeta value method (i.e. the method for improving the signal-to-noise ratio of the weak signal in the background) and the full-peak counting method in the embodiment are compared in signal identification capability
The experiment adopted 40X 10X 5cm3The NaI scintillation detector of (a) above,137the Cs source is placed at a position 100cm away from the detector, and the measured background energy spectrum and the energy spectrum containing the source are shown in figure 2.
The Energy calibration curve in figure 2 is Energy-51.78 +3.14 × channel (kev),137the 661KeV characteristic peak center track address for Cs source is 227. The total energy peak average count rate of the Cs source in the detector is 34s-1Background average count rate of 69s-1. For a common radioactive source, a full-peak counting method is used, a gamma peak of an energy spectrum is fitted to obtain information of characteristic peaks in the energy spectrum, such as peak position, full width at half maximum and the like, and then an energy 3 sigma fluctuation interval [ mu-42 Ch, mu +42Ch ] is selected]The count interval was analyzed and compared to the tail subtraction method of fig. 1. The tail deduction method firstly calculates and selects different counting intervals [ mu-x, mu + x]And selecting x corresponding to the maximum signal-to-noise fluctuation ratio zeta as the counting track width.
TABLE 1 count fluctuation and SNR for different track widths
As can be seen from table 1, the net count increases with increasing x. However, since the absolute value of the background fluctuation is also increasing, the net count relative fluctuation tends to decrease first and then increase. The signal-to-noise ratio decreases with increasing x. The parameter ζ for the identification signal increases and then decreases. ζ had a maximum value of 1035.1 when x was 10, the net count relative fluctuation was 4.1%, and the signal to noise floor ratio was 1.02. When the selected interval x is 3 sigma (x is 21), the zeta value is 612.0, the net count relative fluctuation is 5.1%, and the signal-to-noise floor ratio is 0.482. When x is 10, the optimal signal identification capability can be obtained. By comparison in table 1, it can also be seen that the zeta-value method also allows better signal-to-noise ratio and relative statistical fluctuations of the signal. The zeta value method enables the signal-to-noise ratio to be better while obtaining better statistical fluctuation, increases the difference between the source signal measurement data and the background data, and greatly improves the signal identification capability.
The left side and the right side of the equation (11) are respectively drawn into curves, and the intersection point is the numerical solution of the equation. The experimental value curve of ζ is compared to the curves on the left and right sides of the equation, see fig. 3.
As can be seen from fig. 3, x is 10 when ζ has the maximum value, and the counting interval is [ μ -10Ch, μ +10Ch ]. The curve is drawn from the left and right sides of the theoretical formula (11), and the intersection point position is between [9,10], approximately 9.7, and better fits the experimental value x of 10.
2.2 stability of x when Zeta value is maximized
In order to further verify the reliability of the zeta value method, the zeta value method is carried out under the same condition137The Cs source was measured ten times, and the fluctuation distribution of the x values in the upper and lower domains was obtained when the ζ value was maximized, as shown in table 2.
TABLE 2 x distribution at maximum values of several measurements ζ
Remarking: in Table 2, x @ ζ max is indicated at the ζ maximum; x @3 σ is the gaussian distribution of the signal, and the value of x corresponding to 3 σ is taken.
As can be seen from table 2, in the ten measurements, the x value dispersion is small when the zeta value takes the maximum value, the obtained net count fluctuation is smaller than the count when the full peak counting method selects 3 σ as the interval, and the signal-to-noise ratio obtained by using the zeta value method is much larger than the signal-to-noise ratio of the conventional method selecting 3 σ as the interval.
As can be seen from fig. 4, for a plurality of measurements under the measurement conditions, the average value of x when ζ is taken as the maximum value is 9.7 (standard deviation σ is 0.67), which is highly consistent with the value of 9.7 of the curve intersection point in fig. 3, indicating that the ζ value method has better stability.
2.3 Effect of different Signal Strength on x
For weak sources of different intensities in the measured spectrum, the signal-to-noise ratio varies as the intensity of the weak source changes. Changing the distance between the radioactive source and the detector can simulate the change rule of x under different signal intensities in the background, as shown in figure 5.
As can be seen from fig. 5, the zeta value at different signal intensities (i.e. at different source distances) has a substantially constant trend with x, increasing first and decreasing second, and the maximum zeta value is within a small range around x-9.7. The more accurate values of x for the maximum values of ζ are shown in table 3.
TABLE 3 variation of x at maximum zeta value for different signal strengths
Table 3 shows the zeta-change with x for different signal strengths. It can be seen in table 3 that x at which ζ assumes its maximum value remains well stabilized, fluctuating in the 8,10 range, and is hardly affected by the source signal intensity count, even though the source intensity is lower and lower.
Comparing the results of selecting track width by Zeta value method and selecting 3 sigma as track width by full peak counting method, and к is the net count relative fluctuationsAnd signal-to-noise ratio Rs/nAre superior to the method of using 3 sigma to select track width, see fig. 6 and 7. it can also be seen from table 3 that the relative fluctuation к of the signalsReduced by at least 1/3, signal-to-noise ratio Rs/nImproved by more than 3 times.
The result shows that the zeta value method has obvious effects on improving the signal-to-noise ratio, reducing the statistical fluctuation of signals and increasing the recognition capability of weak signals in the background.
Since the energy resolution can be seen as constant for a particular detector, and x fluctuates in a small range around 9.7 when ζ takes the maximum value, the value of x can be expressed by the standard deviation σ of the full energy peak. It was calculated that the value of the counting interval x at which ζ of the detector used in this example assumes the maximum value was approximately [ μ -1.38 σ, μ +1.38 σ ]. That is, the counting interval x where the influence ζ takes the maximum value is related only to the shape of the gaussian peak in the energy spectrum, and is not related to the height of the peak. When the energy resolution of the detector is changed or the used detector is not the same type, the counting interval x when zeta takes the maximum value is determined again.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.
Claims (6)
1. A background medium and weak signal to noise ratio improving method is characterized by comprising the following steps:
(1) the source signal identification capability ζ of the detector is defined, as shown in the following equation (5),
in the formula, NnAs a count of background, NsCounting the source signals;
the maximum value of ζ can be found from the derivative of equation (5) being zero, i.e., d ζ is 0,
(2) x tracks are symmetrically selected around the central track address mu, and the upper domain and the lower domain are [ mu-x, mu + x]Then the source signal NsThe counts in the count interval are represented as an integral function of the track address t,
in the formula (7), NsμThe number of the channel address and the signal center is set as a constant A; the differential dN of the source signal with xsIn order to realize the purpose,
(3) let the density function of background count with track address be f (Ch), and under the condition of no other peak interference, regard the density function f (Ch) as linear variation with track address, let the background count NnHas a function of Nn＝2NnμX, then NnThe differential of (a), i.e., the density function f (ch), is shown in the following formula (9):
dNn＝2Nnμ·dx＝f(Ch) (9)；
in the formula (9), NnμThe count of the background center track address is approximately constant and is set as C, and the following are:
dNn＝2Cdx (10)；
mixing dNsAnd dNnWhen the formula (6) is substituted, then
(4) When a proper x value is selected to satisfy the formula (11), the signal-to-noise ratio and the relative fluctuation in the counting interval can be well balanced.
2. The method for improving the signal-to-noise ratio of the weak signal in the background according to claim 1, wherein in the step 1, the signal-to-noise ratio and the weight of the relative random fluctuation to the source signal identification capability are assumed to be the same.
3. The method for improving the signal-to-noise ratio of the weak signal in the background according to claim 1 or 2, wherein in the step 1, a source signal identification capability ζ of the detector is defined, as shown in the following formula (1),
in the formula (1), Rs/n-the signal-to-noise ratio;
κs-relative random fluctuations of the signal;
κn-relative random fluctuations in background;
setting the total count of source signal and background to NgBackground count is NnThen the source signal counts NsIn order to realize the purpose,
Ns＝Ng-Nn (2)；
thus, the source signal relative fluctuation кsAnd relative fluctuation к of backgroundnRespectively, are as follows,
in formula (3), σsNet counts fluctuations for the source signal;
in the formula (4), σnThe background fluctuation;
then, ζ can be expressed as,
the maximum value of ζ can be found from the derivative of equation (5) being zero, i.e., d ζ is 0,
4. the background medium-weak signal to noise ratio improving method according to any one of claims 1 to 3, wherein in the step 4, the formula (11) is a transcendental equation, and the value x is obtained by drawing and solving curves on two sides, so that the signal to noise ratio and the relative fluctuation in the obtained counting interval can be well balanced.
5. Use of the method according to any of the preceding claims 1 to 4.
6. Use according to claim 5, characterized in that the method is used for the determination of a radiation signal.
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